Канал: Ullman First Year Calculus

Math 152 Workshop 6 solutions

Math 152 Workshop 6 solutions

Math 152 Workshop 3

Math 152 Workshop 3

Math 152 workshop 2

Math 152 workshop 2

Surface of revolution non zero axes

Surface of revolution non zero axes

Workshop 1 152 Sp21

Workshop 1 152 Sp21

Arc length supplement Arc length in y

Arc length supplement Arc length in y

Arc length supplement Arc length intro revised

Arc length supplement Arc length intro revised

What's in an integral?

What's in an integral?

Complex numbers The most amazing fact in all of mathematics

Complex numbers The most amazing fact in all of mathematics

Complex numbers The complex plane

Complex numbers The complex plane

Complex numbers Seventh roots of a complex number

Complex numbers Seventh roots of a complex number

Complex numbers Real and imaginary part examples

Complex numbers Real and imaginary part examples

Complex numbers Multiple exponential forms of same complex number

Complex numbers Multiple exponential forms of same complex number

Complex numbers Introduction

Complex numbers Introduction

Complex numbers Fourth roots of 5

Complex numbers Fourth roots of 5

Complex numbers Cube roots of 1

Complex numbers Cube roots of 1

Complex numbers Complex numbers in polar form

Complex numbers Complex numbers in polar form

Complex numbers Writing complex numbers in exponential form

Complex numbers Writing complex numbers in exponential form

Calc 1 intro for u sub and area

Calc 1 intro for u sub and area

Polar coordinates Conversion formulas and polar to rectangular example

Polar coordinates Conversion formulas and polar to rectangular example

Polar coordinates Converting polar into rectangular, with equivalency chart

Polar coordinates Converting polar into rectangular, with equivalency chart

Polar coordinates Converting rectangular equations into polar equations, with examples

Polar coordinates Converting rectangular equations into polar equations, with examples

Polar coordinates Graph folium r equal sin 3 theta

Polar coordinates Graph folium r equal sin 3 theta

Polar coordinates Graphing polar equations, r equals theta example

Polar coordinates Graphing polar equations, r equals theta example

Polar coordinates Introduction

Polar coordinates Introduction

Polar coordinates Points in the plane

Polar coordinates Points in the plane

Polar coordinates Rectangular to polar

Polar coordinates Rectangular to polar

Polar coordinates Arc length, circumference of offset r equals 2 cos theta circle example

Polar coordinates Arc length, circumference of offset r equals 2 cos theta circle example

Polar coordinates Area between polar curves

Polar coordinates Area between polar curves

Polar coordinates Area between r equals 1 and r equals 2 cos theta

Polar coordinates Area between r equals 1 and r equals 2 cos theta

Polar coordinates Area bounded by y equals plus or minus x and y equals root 2, as a polar integra

Polar coordinates Area bounded by y equals plus or minus x and y equals root 2, as a polar integra

Polar coordinates Area inside curve formula

Polar coordinates Area inside curve formula

Polar coordinates Area inside one petal of trifolium

Polar coordinates Area inside one petal of trifolium

Polar coordinates Area inside r equals theta plus 1

Polar coordinates Area inside r equals theta plus 1

Polar coordinates Area of rectangle and sliced circle

Polar coordinates Area of rectangle and sliced circle

Fundamental Theorem of Calculus Theorem Part II examples

Fundamental Theorem of Calculus Theorem Part II examples

Fundamental Theorem of Calculus Theorem Part I existence of antiderivative

Fundamental Theorem of Calculus Theorem Part I existence of antiderivative

Fundamental Theorem of Calculus Initial value problem

Fundamental Theorem of Calculus Initial value problem

Fundamental Theorem of Calculus Integration of a rate of change

Fundamental Theorem of Calculus Integration of a rate of change

Fundamental Theorem of Calculus Theorem Part I examples

Fundamental Theorem of Calculus Theorem Part I examples

Fundamental Theorem of Calculus Theorem Part II evaluation with examples

Fundamental Theorem of Calculus Theorem Part II evaluation with examples

Definite integral Average value

Definite integral Average value

Definite integral Definition of definite integral, limit of as norm P approaches zero

Definite integral Definition of definite integral, limit of as norm P approaches zero

Definite integral Examples showing integral properties

Definite integral Examples showing integral properties

Definite integral Integral properties

Definite integral Integral properties

Definite integral min max property

Definite integral min max property

Definite integral Using geometry to find definite integrals

Definite integral Using geometry to find definite integrals

Definite integral Integrals of constant, x, and x squared

Definite integral Integrals of constant, x, and x squared

Parametric curves Arc length, surface area, speed

Parametric curves Arc length, surface area, speed

Parametric curves Tangent line to parametric curve

Parametric curves Tangent line to parametric curve

Parametric curves Alternative parameterization of a circle

Parametric curves Alternative parameterization of a circle

Parametric curves Write parameterized line given two points

Parametric curves Write parameterized line given two points

Parametric curves Cycloid

Parametric curves Cycloid

Parametric curves e t sin t, e t cos t

Parametric curves e t sin t, e t cos t

Parametric curves Eliminate parameter

Parametric curves Eliminate parameter

Parametric curves Ellipse

Parametric curves Ellipse

Parametric curves Explanation of parametric curves

Parametric curves Explanation of parametric curves

Parametric curves Line as a fixed point and a direction

Parametric curves Line as a fixed point and a direction

Parametric curves Parameterization of a circle with example

Parametric curves Parameterization of a circle with example

Parametric curves Parameterize line, example with point 3 negative 1 and slope 4

Parametric curves Parameterize line, example with point 3 negative 1 and slope 4

Parametric curves Projectile motion

Parametric curves Projectile motion

Arc lenth and surface area Arc length 1 twelvth x cubed plus x to the minus 1

Arc lenth and surface area Arc length 1 twelvth x cubed plus x to the minus 1

Arc lenth and surface area Surface of revolution of square root of x

Arc lenth and surface area Surface of revolution of square root of x

Arc lenth and surface area Introduction and arc length explanation

Arc lenth and surface area Introduction and arc length explanation

Arc lenth and surface area Surface area explanation

Arc lenth and surface area Surface area explanation

Area and finite sums Area approximations, upper, lower, right, and left sums

Area and finite sums Area approximations, upper, lower, right, and left sums

Area and finite sums Area of 5 minus x squared on interval 1 to 2, upper and lower sums

Area and finite sums Area of 5 minus x squared on interval 1 to 2, upper and lower sums

Area and finite sums Area under a rate of change function explanation

Area and finite sums Area under a rate of change function explanation

Area and finite sums Average value of sin x on 0 to pi

Area and finite sums Average value of sin x on 0 to pi

Area and finite sums closed forms for sum of the first n integers, squares, and cubes

Area and finite sums closed forms for sum of the first n integers, squares, and cubes

Area and finite sums Displacement and total distance using table values

Area and finite sums Displacement and total distance using table values

Area and finite sums Displacement as area enclosed by velocity function

Area and finite sums Displacement as area enclosed by velocity function

Area and finite sums Examples of using area summation formula

Area and finite sums Examples of using area summation formula

Area and finite sums Find exact area under x squared as limit of Riemann sum

Area and finite sums Find exact area under x squared as limit of Riemann sum

Area and finite sums Hint on inscribed polygon problem

Area and finite sums Hint on inscribed polygon problem

Area and finite sums Intro to sigma notation

Area and finite sums Intro to sigma notation

Area and finite sums limit of 1 over n squared times sum of k

Area and finite sums limit of 1 over n squared times sum of k

Area and finite sums right endpoint approximation of area as a summation

Area and finite sums right endpoint approximation of area as a summation

Area and finite sums Summation properties and examples

Area and finite sums Summation properties and examples

Zero zero limits with Taylor Series

Zero zero limits with Taylor Series

Antiderivatives Antiderivative examples 1

Antiderivatives Antiderivative examples 1

Antiderivatives Antiderivatives and indefinite integrals

Antiderivatives Antiderivatives and indefinite integrals

Antiderivatives Initial value problem intro and f prime equal cos x example

Antiderivatives Initial value problem intro and f prime equal cos x example

Antiderivatives Initial value problem using rectilinear motion

Antiderivatives Initial value problem using rectilinear motion

Antiderivatives Initial value problem with second derivative

Antiderivatives Initial value problem with second derivative

Antiderivatives Linearity rule and more antiderivative examples

Antiderivatives Linearity rule and more antiderivative examples

Workshop 9 solutions

Workshop 9 solutions

Applied Optimization Where to build new road

Applied Optimization Where to build new road

Applied Optimization Number problem

Applied Optimization Number problem

Applied Optimization Picture frame

Applied Optimization Picture frame

Applied Optimization Open top box

Applied Optimization Open top box

Applied Optimization Rectangle inscribed in parabola

Applied Optimization Rectangle inscribed in parabola

Applied Optimization Farmer problem

Applied Optimization Farmer problem

Applied Optimization Introduction

Applied Optimization Introduction

Power Series Determine which points could be center of series

Power Series Determine which points could be center of series

Taylor and Maclaurin Series Find the 26th and 27th derivatives

Taylor and Maclaurin Series Find the 26th and 27th derivatives

Taylor and Maclaurin Series Introduction

Taylor and Maclaurin Series Introduction

Taylor and Maclaurin Series M4 for square root of x plus 1

Taylor and Maclaurin Series M4 for square root of x plus 1

Taylor and Maclaurin Series Maclaurin polynomials, use M4 to integrate e to the negative x squared

Taylor and Maclaurin Series Maclaurin polynomials, use M4 to integrate e to the negative x squared

Taylor and Maclaurin Series Maclaurin series for e to the x, sin, and cos

Taylor and Maclaurin Series Maclaurin series for e to the x, sin, and cos

Taylor and Maclaurin Series Remainder and error bound

Taylor and Maclaurin Series Remainder and error bound

Taylor and Maclaurin Series sin x with center pi over 6

Taylor and Maclaurin Series sin x with center pi over 6

Taylor and Maclaurin Series Taylor and Maclaurin formulas

Taylor and Maclaurin Series Taylor and Maclaurin formulas

Taylor and Maclaurin Series x squared e to the x, and finding fifth derivative

Taylor and Maclaurin Series x squared e to the x, and finding fifth derivative

Power Series Change interval of convergence of power series

Power Series Change interval of convergence of power series

LHopital's Rule x to the x

LHopital's Rule x to the x

LHopital's Rule x times ln x

LHopital's Rule x times ln x

LHopital's Rule x minus sin x over x cubed

LHopital's Rule x minus sin x over x cubed

LHopital's Rule non example

LHopital's Rule non example

LHopital's Rule ln x over x squared

LHopital's Rule ln x over x squared

LHopital's Rule Introduction and sin 3x over 4x

LHopital's Rule Introduction and sin 3x over 4x

LHopital's Rule 1 plus 2 over x to the x

LHopital's Rule 1 plus 2 over x to the x

LHopital's Rule 1 over sin x minus 1 over x

LHopital's Rule 1 over sin x minus 1 over x

Graph sketching x to the 4th minus 4 x cubed plus 10

Graph sketching x to the 4th minus 4 x cubed plus 10

Graph sketching x squared plus 4 over 2x

Graph sketching x squared plus 4 over 2x

Graph sketching Second derivative test examples

Graph sketching Second derivative test examples

Graph sketching Process of sketching a graph

Graph sketching Process of sketching a graph

Graph sketching Explanation of second derivative test

Graph sketching Explanation of second derivative test

Graph sketching Explanation of concavity

Graph sketching Explanation of concavity

Graph sketching e to the 2 over x

Graph sketching e to the 2 over x

Monotone Functions and the First Derivative Test Example 1 using first derivative test

Monotone Functions and the First Derivative Test Example 1 using first derivative test

Monotone Functions and the First Derivative Test Example 2 using first derivative test

Monotone Functions and the First Derivative Test Example 2 using first derivative test

Monotone Functions and the First Derivative Test First derivative test explanation

Monotone Functions and the First Derivative Test First derivative test explanation

Monotone Functions and the First Derivative Test Monotone function theorem

Monotone Functions and the First Derivative Test Monotone function theorem

Monotone Functions and the First Derivative Test x minus 1 over x squared plus 8

Monotone Functions and the First Derivative Test x minus 1 over x squared plus 8

Power Series integration and differentiation Calculuate sum from 1 to inf of n over 5 to n minus 1

Power Series integration and differentiation Calculuate sum from 1 to inf of n over 5 to n minus 1

Power Series integration and differentiation Find series for arctan x and ln 1 plus x

Power Series integration and differentiation Find series for arctan x and ln 1 plus x

Power Series integration and differentiation Introduction

Power Series integration and differentiation Introduction

Power Series First Batch Long, boring, but necessary introduction to power series

Power Series First Batch Long, boring, but necessary introduction to power series

Power Series First Batch 1 over 1 minus 2x

Power Series First Batch 1 over 1 minus 2x

Power Series First Batch 1 over 7 minus x with center 3

Power Series First Batch 1 over 7 minus x with center 3

Power Series First Batch 2 over five plus x cubed

Power Series First Batch 2 over five plus x cubed

Power Series First Batch find IOC of x minus 5 to the n over 4 to the n times n alternating

Power Series First Batch find IOC of x minus 5 to the n over 4 to the n times n alternating

Power Series First Batch find IOC of x to the n over 2 to the n

Power Series First Batch find IOC of x to the n over 2 to the n

Power Series First Batch Geometric series expansion

Power Series First Batch Geometric series expansion

Power Series First Batch radius of convergence n to the 2n x to the n over 2n factorial

Power Series First Batch radius of convergence n to the 2n x to the n over 2n factorial

Mean Value Theorem Solve initial value problem

Mean Value Theorem Solve initial value problem

Mean Value Theorem Use MVT to find maximum possible increase

Mean Value Theorem Use MVT to find maximum possible increase

Mean Value Theorem Verify that mean value theorem applies

Mean Value Theorem Verify that mean value theorem applies

Mean Value Theorem x to the two thirds

Mean Value Theorem x to the two thirds

Mean Value Theorem Explanation of MVT and Rolles Theorem

Mean Value Theorem Explanation of MVT and Rolles Theorem

Mean Value Theorem Find point where instant velocity equals average velocity

Mean Value Theorem Find point where instant velocity equals average velocity

Mean Value Theorem Make function satisfy hypotheses of MVT

Mean Value Theorem Make function satisfy hypotheses of MVT

Mean Value Theorem only derivative of constant is zero on interval

Mean Value Theorem only derivative of constant is zero on interval

Conditional Convergence and Alternating Series Proof that 0 less than S less than a1

Conditional Convergence and Alternating Series Proof that 0 less than S less than a1

Conditional Convergence and Alternating Series Verify error bound for alt harmonic series

Conditional Convergence and Alternating Series Verify error bound for alt harmonic series

Conditional Convergence and Alternating Series Alternating series test, with example

Conditional Convergence and Alternating Series Alternating series test, with example

Conditional Convergence and Alternating Series Definitions of cond convergence and alt series

Conditional Convergence and Alternating Series Definitions of cond convergence and alt series

Conditional Convergence and Alternating Series Error bound for alternating series

Conditional Convergence and Alternating Series Error bound for alternating series

Conditional Convergence and Alternating Series Find smallest N to approximate 1 over square root o

Conditional Convergence and Alternating Series Find smallest N to approximate 1 over square root o

Extreme values and critical points Critical points, Fermas Theorem, and the optimization of cont f

Extreme values and critical points Critical points, Fermas Theorem, and the optimization of cont f

Extreme values and critical points Definition of extreme values

Extreme values and critical points Definition of extreme values

Extreme values and critical points Definition of local extrema

Extreme values and critical points Definition of local extrema

Extreme values and critical points Extreme Value theorem, with non examples

Extreme values and critical points Extreme Value theorem, with non examples

Extreme values and critical points Optimize a piecewise function

Extreme values and critical points Optimize a piecewise function

Extreme values and critical points Optimize fourth degree quartic polynomial on closed interval

Extreme values and critical points Optimize fourth degree quartic polynomial on closed interval

Extreme values and critical points Optimize function with absolute value expression

Extreme values and critical points Optimize function with absolute value expression

Extreme values and critical points Optimize trig function on closed interval

Extreme values and critical points Optimize trig function on closed interval

Extreme values and critical points optimize x minus 1 to the minus two thirds

Extreme values and critical points optimize x minus 1 to the minus two thirds

Absolute convergence, ratio and root tests Ratio and root tests explanation

Absolute convergence, ratio and root tests Ratio and root tests explanation

Absolute convergence, ratio and root tests Ratio test inconclusive examples

Absolute convergence, ratio and root tests Ratio test inconclusive examples

Absolute convergence, ratio and root tests root test, n over 2n plus 3 to the n

Absolute convergence, ratio and root tests root test, n over 2n plus 3 to the n

Absolute convergence, ratio and root tests sin n over n squared

Absolute convergence, ratio and root tests sin n over n squared

Absolute convergence, ratio and root tests Sum of alternating 1 over n squared

Absolute convergence, ratio and root tests Sum of alternating 1 over n squared

Absolute convergence, ratio and root tests 2 to the n over n factorial

Absolute convergence, ratio and root tests 2 to the n over n factorial

Absolute convergence, ratio and root tests alternating n factorial over 1000 to the n

Absolute convergence, ratio and root tests alternating n factorial over 1000 to the n

Absolute convergence, ratio and root tests How to find limit of 1 plus 1 over n to the n

Absolute convergence, ratio and root tests How to find limit of 1 plus 1 over n to the n

Absolute convergence, ratio and root tests n to the n over n factorial

Absolute convergence, ratio and root tests n to the n over n factorial

Absolute convergence, ratio and root tests Positive term series, defn of absolute convergence, abs

Absolute convergence, ratio and root tests Positive term series, defn of absolute convergence, abs

Linear approximation Change in surface area of a cube

Linear approximation Change in surface area of a cube

Linear approximation cube root of 7 9

Linear approximation cube root of 7 9

Linear approximation Differential form of a derivative

Linear approximation Differential form of a derivative

Linear approximation Error in measurement of volume of sphere

Linear approximation Error in measurement of volume of sphere

Linear approximation Explanation of linearization and differentials

Linear approximation Explanation of linearization and differentials

Linear approximation linearization of square root of x plus 1

Linear approximation linearization of square root of x plus 1

Linear approximation sin pi over 6 plus 01

Linear approximation sin pi over 6 plus 01

Integral test, DCT, LCT sin 1 over n over n

Integral test, DCT, LCT sin 1 over n over n

Integral test, DCT, LCT p series

Integral test, DCT, LCT p series

Integral test, DCT, LCT n squared over n cubed minus n

Integral test, DCT, LCT n squared over n cubed minus n

Integral test, DCT, LCT ln n over n to the 1 1

Integral test, DCT, LCT ln n over n to the 1 1

Integral test, DCT, LCT LCT and 1 over square root of 4n squared plus 1

Integral test, DCT, LCT LCT and 1 over square root of 4n squared plus 1

Integral test, DCT, LCT Integral test and 1 over n ln n

Integral test, DCT, LCT Integral test and 1 over n ln n

Integral test, DCT, LCT Instructions on DCT and LCT proofs

Integral test, DCT, LCT Instructions on DCT and LCT proofs

Integral test, DCT, LCT Explanation of DCT

Integral test, DCT, LCT Explanation of DCT

Integral test, DCT, LCT Absolute sin n factorial over n squared plus 1

Integral test, DCT, LCT Absolute sin n factorial over n squared plus 1

Integral test, DCT, LCT 2 to the n over 3 to the n minus 1

Integral test, DCT, LCT 2 to the n over 3 to the n minus 1

Integral test, DCT, LCT 1 over square root n 3 to the n

Integral test, DCT, LCT 1 over square root n 3 to the n

Related Rates Conical tank

Related Rates Conical tank

Related Rates Falling ladder

Related Rates Falling ladder

Related Rates Inflating balloon

Related Rates Inflating balloon

Related Rates Intro definitions and examples

Related Rates Intro definitions and examples

Related Rates Lamp post

Related Rates Lamp post

Related Rates Rowboat

Related Rates Rowboat

Related Rates The Ullman Method TM

Related Rates The Ullman Method TM

Related Rates Title card

Related Rates Title card

Derivatives of inverse and inverse trig functions Using inverse function rule for derivative of ar

Derivatives of inverse and inverse trig functions Using inverse function rule for derivative of ar

Derivatives of inverse and inverse trig functions Derivatives of inverses

Derivatives of inverse and inverse trig functions Derivatives of inverses

Derivatives of inverse and inverse trig functions Logarithmic differentiation

Derivatives of inverse and inverse trig functions Logarithmic differentiation

Derivatives of inverse and inverse trig functions Review of inverse trig

Derivatives of inverse and inverse trig functions Review of inverse trig

Derivatives of inverse and inverse trig functions Using implicit differentiation to find derivativ

Derivatives of inverse and inverse trig functions Using implicit differentiation to find derivativ